negative poisson ratio materials and potential in aerospace and defense

8/15/2019 Negative Poisson Ratio Materials and Potential in Aerospace and Defense

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Literature Review: Materials with Negative Poisson'sRatios and Potential Applications to Aerospace andDefence

Q. Liu

Air Vehicles DivisionDefence Science and Technology Organisation

DSTO-GD-0472

ABSTRACT

An auxetic material exhibits exceptional features, which are different from a conventionalmaterial. That is, the auxetic material gets fatter when it is stretched, or becomes smaller whenit is compressed, because it has a negative Poisson’s ratio. This report briefly reviews the latestadvances in research work in auxetic materials, structural mechanisms, properties and

applications, particularly in aerospace and defence.

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© Commonwealth of Australia 2006 AR-013-622 August 2006

APPROVED FOR PUBLIC RELEASE


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Literature Review: Materials with Negative Poisson's

Ratios and Potential Applications to Aerospace andDefence

Executive Summary

Modern technology requires new materials of special properties. One of the reasons forinterest in materials of unusual mechanical properties comes from the fact that they can

be used as matrices to form composites with other materials of other requiredproperties, e.g. electric, magnetic, etc. A new field of endeavour is to study materialsexhibiting negative Poisson’s ratio (NPR). These types of materials get fatter when theyare stretched, or become smaller when compressed, in contrast to conventionalmaterials (like rubber, glass, metals, etc.). Large-scale cellular structures with NPRproperty were first realised in 1982 in the form of two-dimensional silicone rubber oraluminium honeycombs deforming by flexure of the ribs (Gibson, et al, 1982 & 1988).In 1987, Lakes first developed the NPR polyurethane foam with re-entrant structure(Lakes, 1987a and 1987b). This polymeric foam had a Poisson’s ratio of -0.7. These newtypes of materials were named auxetics by Evans (Evans, et al, 1991). “Auxetics” comesfrom the Greek word auxetos, meaning “that which may be increased”.

Studies and experiments have demonstrated that auxetic materials (i.e., materials withNPR) can improve mechanical properties, including shear resistance, indentationresistance and fracture toughness, compared to conventional materials from whichthey are made. These auxetic materials also offer very good sound and vibrationabsorption and could have many potential applications to aerospace and defence areas.

This report briefly reviews the latest advances in research work in auxetic materials,structural mechanisms, properties and applications, particularly in aerospace anddefence. Indeed, these new types of materials have a lot of potential applications toDefence such as personal protective equipments (e.g., protective clothing, body

armour, bullet-proof vest, etc) and others (e.g., “smart” sensors, sonar, panels etc).Also, these materials could potentially be used to build completely new structures withspecial functions. However, more research work needs to be done for furtherunderstanding of these materials and applications to real components. Also, for futurework it is necessary to collaborate with researchers from textile, chemical & biologicalareas to explore the potential applications for protecting military personnel frominjury, or chemical and biological attacks.


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Authors

Qianchu Liu Air Vehicles Division

Qianchu Liu joined Defence Science and Technology Organisation(DSTO) in 1999. After completing his PhD in 1991 at the ViennaUniversity of Technology, Austria, he held various academic

positions at the University of Technology Vienna and theUniversity of Sydney. Currently, he is currently a senior researchscientist in Air Vehicles Division, DSTO. His main researchinterests include fatigue, fracture and corrosion of metallicmaterials, life extension or enhancement, repair of damaged

materials and components of aircraft, material joining, surfacetreatments, laser processing and Non-destructive inspections.

____________________ ________________________________________________


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Contents

1. INTRODUCTION ............................................................................................................... 1

2. MECHANISM, STRUCTURE AND FUNCTIONS OF MATERIALS ...................... 2 2.1 General........................................................................................................................2 2.2 Mechanism and Structure ....................................................................................... 3 2.3 Classifications and Types........................................................................................ 6

3. PROPERTIES OF MATERIALS........................................................................................ 8 3.1 Young’s and Shear Moduli...................................................................................... 8 3.2 Indentation Behaviours ........................................................................................... 9

3.3 Deformation Behaviour......................................................................................... 11 3.4 Fracture Toughness................................................................................................. 12

3.4.1 Fracture Behaviour.................................................................................. 12 3.4.2 Microstructural Morphology................................................................. 15 3.4.3 Crack Resistance...................................................................................... 15

3.5 Damping and Sound Absorption ........................................................................ 18

4. MANUFACTURING METHODS .................................................................................. 19 4.1 Manufacture of Auxetic Foams ............................................................................ 19

4.1.1 Polymeric Foams ..................................................................................... 19 4.1.2 Metallic Foams......................................................................................... 20

4.2 Manufacture of Auxetic Fibres and Composites............................................... 20 4.3 Other Methods and Examples .............................................................................. 22

5. POTENTIAL APPLICATIONS AND LIMITATIONS............................................... 24 5.1 General Applications ............................................................................................. 24

5.1.1 Sensors ...................................................................................................... 24 5.1.2 Biomedicine.............................................................................................. 24 5.1.3 Auxetic Fibre Reinforced Composites.................................................. 25 5.1.4 Structures.................................................................................................. 26

5.2 Potential Applications in Aerospace and Defence........................................... 26

5.2.1 Smart or “Intelligent” Textiles............................................................... 27 5.2.2 Bullet-Proof Helmets and Vests............................................................. 28 5.2.3 Fasteners and Rivets................................................................................ 28 5.2.4 Energy Absorption Material for the Protection of Airborne Cargo

Drops................................................................................................................ 29 5.2.5 Other Applications.................................................................................. 30

5.3 Limitations ............................................................................................................... 30

6. CONCLUSIONS AND RECOMMENDATIONS ....................................................... 31

7. ACKNOWLEDGEMENTS...............................................................................................31


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8. REFERENCES..................................................................................................................... 31

APPENDIX A: RECIPE FOR POLYMERIC FOAMS .................................................... 37


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1. Introduction

Modern technology requires new materials of special properties. One of the reasons forinterest in materials of unusual mechanical properties comes from the fact that they can beused as matrices to form composites with other materials of other required properties, e.g.electric, magnetic, etc. A new field of endeavour is to study materials exhibiting negativePoisson’s ratio (NPR). Large-scale cellular structures with NPR property were first realisedin 1982 in the form of two-dimensional silicone rubber or aluminium honeycombsdeforming by flexure of the ribs (Gibson, et al, 1982 & 1988). In 1987, Lakes1 first developedthe NPR polyurethane foam with re-entrant structure (Lakes, 1987a and 1987b). Thispolymeric foam had a Poisson’s ratio of -0.7. These new types of materials were namedauxetics by Evans2 (Evans, et al, 1991) , which, in contrast to conventional materials (likerubber, glass, metals, etc.), expand transversely when pulled longitudinally and contract

transversely when pushed longitudinally. “Auxetics” comes from the Greek word auxetos,meaning “that which may be increased”. In this report, the term ‘auxetic’ will be used.

People have known about auxetic materials for over 100 years, but have not given themmuch attention. This type of material can be found in some rock and minerals, evenanimal such as the skin covering a cow’s teats. To date, a wide variety of auxetic materialshas been fabricated, including polymeric and metallic foams, microporous polymers,carbon fibre laminates and honeycomb structures. A typical example is a well-knownsynthetic polymer-polytetrafluorothylene (PTFE), which has been in use for many years.Other materials possess the NPR property such as microporous ultra high molecularweight polyethylene (UHMWPE), polypropylene (PP) (Caddock & Evans, 1989; Picklrs, et

al, 1996; Alderson, et al, 2000), several types of rocks (Nur & Simmons, 1969). However,their special characteristics are largely ignored. Only up until recently, Lakes, Evans andother scientists’ work has attracted more attention to these auxetic materials.

These auxetic materials are of interest due to the possibility of enhanced mechanicalproperties such as shear modulus, plane strain fracture toughness and indentationresistance (Lakes, 1987a; Evans, 1990). Therefore, studying these non-conventionalmaterials is indeed important from the point of view of fundamental research and possiblypractical applications, particularly in medical, aerospace and defence industries. In fact,some materials with such anomalous (i.e. NPR) properties have been used in applicationssuch as pyrolytic graphite for thermal protection in aerospace, large single crystals of

Ni3Al in vanes for aircraft gas turbine engines, and so on.

The main objective of this report is to conduct a literature review of the research work inthis field and to provide useful information for potential Defence applications of this typeof material. The result of the program could lead to a new research area, which may bebeneficial to the Australian Defence Force and other areas.

1 A professor from the University of Iowa, USA.

2 A professor from the University of Exeter, UK.


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2. Mechanism, Structure and Functions of Materials

2.1

GeneralIt is well known that Poisson's ratio3 is defined by the ratio of the transverse contractionstrain to the longitudinal extension strain in a simple tension condition (Fung, 1968; Beer,et al, 2001), i.e.,

yy

xx

ε ν

ε = − (1)

Since most engineering materials become thinner in cross section when stretched, asshown in Figure 1 (a), Poisson’s ratio in this situation is positive, typically around 0 to

+0.5. The reason is that the inter-atomic bonds realign with deformation. However, somematerials or structures contract in the transverse direction under uniaxial compression, orexpand laterally when stretched, see Figure 1 (b). These materials or structures are said tohave negative Poisson's ratios (NPR). A typical example is a novel foam structure or anauxetic material, where a material gets fatter when stretched. This behaviour does notcontradict the classical theory of elasticity: based on the thermodynamic considerations ofstrain energy, the Poisson's ratios of isotropic materials can not only take negative values,but can have a range of negative values twice that of positive ones (Fung, 1968). That is,the Poisson's ratio is bounded by two theoretical limits: it must be greater than -1, and lessthan or equal to 0.5, i.e.,

1 0.5ν − < ≤ (2)

The upper bound of the Poisson’s ratio corresponds to rubber-like materials with aninfinite bulk modulus (Lakes, 1987), while the lower bound stands for an infinite shearmodulus.

x

y

Original

geometryOriginal

geometryx

y

(a) (b)

Figure 1 (a) A material deformation with positive Poisson’s ratio and (b) A material deformationwith negative Poisson’s ratio when stretched.

3 Named after the French mathematician, Simeon Poisson (1781-1840).


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2.2 Mechanism and Structure

As stated above, a material with NPR expands (gets fatter) when stretched, as opposed to

most materials, which tend to get thinner. A typical mechanism is shown in Figure 2.When a force pulls the structure in one direction (e.g., here vertically), the structure opensup or expands in the perpendicular direction (here, horizontally), i.e., the structure getsfatter. Based on this simple mechanism, a network-like structure can be built up, as shownin Figure 3, where a 2D structure of such a material consists of a regular array ofrectangular nodules connected by fibrils (Burke, 1997). Deformation of the structure is by‘hinging’ of the fibrils. For the ‘open’ geometry, the cells elongate along the direction ofstretch and contract transversely in response to stretching the network, giving a positive v(refer to Figure 3 (a)). However, the structure is modified to adopt a re-entrant 4 geometry,Figure 3 (b), and the network now undergoes elongation both along and transverse to thedirection of applied load. In other words, this is an auxetic structure.

Pull

Expanded

Stretched

Figure 2 Schematic of basic deformation mechanism in auxetic material.

Figure 4 shows the variation in width plotted against length variation for twopolypropylene (PP) fibres stretched axially. Fibre 1 is a conventional PP fibre and shows a

contraction in width as it is extended, corresponding to a positive Poisson’s ratio (ν).Fibre 2 is processed using extruder temperatures 5 , which lead to the nodule-fibril

microstructure. Its width now increases upon stretching - it displays auxetic behaviour.

For auxetic honeycombs, which are a special subset of auxetic materials, the NPR effect isdue to the geometric layout of the unit cell microstructure, leading to a global stiffeningeffect in many mechanical properties such as in-plane indentation resistance, transverseshear modulus and bending stiffness. Figure 5 shows the deformation mechanism of theauxetic honeycombs along with conventional honeycomb structure. For a conventionalhexagonal geometry (Figure 5 (a)), under the stretch in the y direction the cells elongate

4 Re-entrant is also named as auxetic by Evans et al.

5 Extruder temperature is a temperature during continuous forming of a material (e.g. rubber) by forcing

through a die.


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along the y-axis and close up in the x direction, leading to a positive Poisson’s ratio.However, for an auxetic structure, the cells undergo elongation both parallel andperpendicular to the direction of the applied load.

(a)

(b)

Figure 3 Comparison of deformation behaviours: (a) non-auxetic and auxetic material (after Alderson, 1999; Evans & Alderson, 2000; Lakes, 2001).

Figure 4 Width as a function of length variations for polypropylene fibres (after Stott, et al,2000).


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(a) (b)

Figure 5 Two-dimensional deformation mechanisms, which are subjected to loading in the y-direction: (a) Conventional honeycomb structure (b) Auxetic honeycomb structure (afterEvans & Alderson, 2000a; Evans & Alderson, 2000b).

For auxetic microporous polymer, the characteristics of the microstructure can beinterpreted by a simple 2D model, as shown in Figure 6. This basically consists of aninterconnected network of nodules and fibrils. If a tensile load is applied, the fibrils causelateral nodule translation, leading to a strain-dependent negative Poisson’s ratio.

Nodules

Fibrils

(a) (b)

Figure 6 Schematic of the microstructure of a typical auxetic polymer. (a) The polymer at restand (b) The polymer at the tensile load (After Caddock & Evans, 1989; Evans &Caddock, 1989).


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2.3 Classifications and Types

Materials with NPR expand in all directions when pulled in only one, therefore behavingin an opposite manner compared to conventional materials. Foams and honeycombs are aspecial subset of auxetic materials. The NPR effect is due to the geometric layout of theunit cell microstructure, leading to a global stiffening effect in many mechanical propertiessuch as in-plane indentation resistance, transverse shear modulus and bending stiffness.Under compression, the increase of relative density leads also to an enhanced mechanicalbehaviour. Auxetic honeycomb cores can be also used effectively to manufacture curvedsandwich panels because of their synclastic curvature feature due to the NPR effect.

A variety of auxetic materials and structures have been discovered, manufactured orsynthesised within about the last twenty years, ranging from the molecular level, up

through the microscopic, and right up to genuinely macroscopic level. Figure 7 shows thatthe major classes of materials (polymers, composites, metals and ceramics) now exist inauxetic form and that natural and synthetic auxetic materials are known over severalorders of magnitude of stiffness, or Young's modulus, E. The detail of the review fromnaturally to man-made auxetic materials can be seen in Evans & Alderson’s paper (2000b).

Figure 7 Classes of materials in auxetic form (after Stott, et al, 2000).


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Nearly, all conventional materials, including foams, exhibit a positive Poisson’s ratio.Recently, Lakes created a new type of foam material that exhibits a NPR (Lakes, 1987a &b). This material was produced by transformation of the conventional cell structure (Figure

8 (a)), so that the cell ribs protrude inward rather than outward, i.e. a re-entrant structure,as shown in Figure 8 (b). When the vertically protruding ribs are under tension, the ribs inthe lateral directions will tend to move out, leading to lateral expansion. However, whencompression is applied, the ribs will bend inward further, thus resulting in lateralcontraction in response to axial compression. Based on this model, polymeric foams withNPRs could be made.

(b)(a)

Figure 8 Idealised models for foam cells. (a) Conventional cell. (b) Re-entrant cell (after Lakes &Witt, 2002).


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3. Properties of Materials

Materials with NPRs have the following special properties:(1) High in-plane indentation resistance;(2) Good fracture toughness;(3) High transverse shear modulus; and,(4) High dynamic properties.

3.1 Young’s and Shear Moduli

Another special feature of auxetic materials is to have higher resistance to shear strain,caused by twisting or tearing forces. Shear resistance is particularly important in structuralcomponents such as sheets or beams in buildings, cars and aircraft. This feature can be

qualitatively explained by the relations among the shear (or rigidity) modulus G, theYoung’s modulus E, and bulk modulus K (the inverse of the compressibility) and

Poisson’s ratio (ν). For isotropic material, the relations are (Fung, 1968; Beer, et al, 2001):

3K(1 2 )G

2(1 )

− ν=

+ν (3)

and

)21(3)1(2 ν ν −=+= K G E . (4)

In conventional isotropic materials, Young’s modulus (E) is at least twice the shearmodulus (G). However, when the Poisson’s ratio becomes negative, the two moduli

become close until, at ν = -0.5, they are equal. In other words, the material becomes highlycompressible but difficult to shear; its bulk modulus and Young’s modulus are much less

than its shear modulus. Beyond ν = -0.5, the shear modulus actually exceeds the elasticmodulus (Choi & Lakes, 1992). For example, a solid with ν = -1 would be difficult to shearbut easy to deform volumetrically: G>>K. However, if the Poisson’s ratio approaches thepositive 0.5, as in rubbery solids, the bulk modulus (K) greatly exceeds the shear modulus(G) and the material is referred to as incompressible: G


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Figure 9 Young's modulus as it depends upon initial relative density and upon volumetriccompression ratio; initial relative density. Solid squares - 0.1; open diamonds - 0.09;solid diamonds - 0.08; open squares - 0.04 (after Choi & Lakes, 1992).

Figure 10 Young's modulus as a function of permanent volumetric compression ratio for annealedand non annealed copper foam at a strain of 0.5%; non-treated, non-annealed; heattreated, annealed (after Choi & Lakes, 1992).

3.2 Indentation Behaviours

Auxetic materials do not dent as easily as non-auxetic materials and so have moreresistance to indentations. When a non-auxetic material is subjected to impact loading, the


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force compresses the material, and the material is compensated by spreading in directionsperpendicular to and away from the direction of the impact (see arrows in Figure 11 (a)).However, when an object hits an auxetic material and compresses it in one direction, the

auxetic material also contracts laterally — material ‘flows’ into (compresses towards) thevicinity of the impact, as shown in Figure 11 (b). This creates an area of denser material,which is more resistant to indentation. The investigation showed that re-entrant foams had

higher yield strength (σy) and less stiffness (E) than conventional foams with the sameoriginal relative density. It has also been further proven that re-entrant foams indeeddensify under indentation due to increase in shear stiffness (Smith, et al, 1999).

Figure 11 Schematic of deformation behaviours when both non-auxetic and auxetic materials aresubject to impact compressive loading (after Alderson, 1999; Evans & Alderson, 2000).

Based on the classic elasticity theory (Timoshenko & Goodier, 1970), the indentation

resistance or hardness of an isotropic material is inversely proportional to (1-ν 2 ), that is:

2(1 )

E H

v

γ

⎡ ⎤∝ ⎢ ⎥−⎣ ⎦

(5)

Where γ = 1 stands for uniform pressure distribution and γ = 2/3 is Hertzian indentation.

For a given value of E, the indentation resistance increases with negative Poisson’s ratio

(ν). If the ν value approaches -1, the hardness becomes infinite. Hardness has beeninvestigated for many of the synthetic auxetic materials produced to date andenhancements have been found across the board in materials as diverse as polymeric andmetallic foams (Chan & Evens, 1998; Lakes & Elms, 1993), carbon fibre compositelaminates (Coenen, et al, 2001b) and microporous polymers (Alderson, et al, 2000). Forexample, the hardness of the auxetic microporous ultra high molecular weightpolyethylene (UHMWPE) was improved by up to a factor of 2 over conventionalUHMWPE (Alderson, et al, 1994 & 2000). In addition, at lower loading (e.g., 10 ~ 100N),the indentation test showed that it was more difficult to indent and the hardness wasincreased by up to a factor of 8 if the Poisson’s ratio was changed from approximately 0 to-0.8 (Alderson, 1994; Yang, et al, 2004).


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3.3 Deformation Behaviour

Very recent investigations into low velocity impact of auxetic carbon fibre laminates have

also shown enhancements in energy absorption of up to a third for the first failure point(Coenen, et al, 2001a). Cold work in a re-entrant foam material has some effects due to thetriaxial compression during manufacturing.

However, the annealing has an obvious effect on Young’s modulus. Figure 12 shows thestrain-stress relationships for conventional and re-entrant foam materials. The annealingnormally reduces Young’s modulus at a given volumetric compression ratio (refer to Figure10). In other words, the material becomes less stiff. So that re-entrant copper foam is lessstiff than the conventional foam from which it was derived. For the conventional copperfoams the properties in tension and compression are similar. However, the re-entrant foamsshow dissimilar behaviours in tension and compression. In addition, in both tension and

compression, the conventional and re-entrant foams exhibit a rather long plateau above theproportional limit. This behaviour is attributed to the plastic hinge formation of cell ribs(Choi & Lakes, 1992). From Figure 12, it can also be seen that the conventional foam hassome strain-hardening tendency, but the re-entrant foam does not. Therefore, this materialcan be reasonably assumed as an elastic-perfectly plastic material in modelling.

Figure 12 Stress- strain relationships for conventional and re-entrant foams. Initial relativedensity: 0.08. Solid symbols: annealed. Open symbols: not annealed. Squares:

conventional foam, volumetric compression 1. Triangles: re-entrant foam, volumetric

compression 2.0. O Circles: re-entrant foam, volumetric compression 2.5. Diamonds:re-entrant foam, volumetric compression 3.0 (after Choi & lakes, 1992).


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3.4 Fracture Toughness

3.4.1 Fracture Behaviour

Fracture behaviour of both conventional and re-entrant foam in tension is brittle-like. Thefailure occurs abruptly without necking (Gibson & Ashby, 1988; Choi & Lakes, 1992). Onthe scale of the dimension of the cells, a crack extends in a discrete way; each stepadvances the crack by one cell width (Maiti, et al, 1984). When the stress at a crack tip ishigh enough in the cell edge or wall, a local fracture occurs and the crack advances.

However, the crack extension can take place in two different ways (Ashby, 1983):(1) Through the bending failure of the non-vertical cell wall or edges (Figure 13 (a)); or(2) By the fracture of the vertical elements under a combined tension and bending moment(Figure 13 (b)).

(a) (b)

Figure 13 Schematic of crack extension manners in a cellular solid. (a) Through the bending failure mode of the non-vertical cell elements and (b) Through the tensile fracture of thevertical cell elements (after Maiti, et al, 1984).

Since the cells in conventional foams have a non-zero size, cracks in the material can not be

perfectly sharp (Figure 14). The non-singular stress field at distance r (for / 2tipr r > ) for acrack of 2a with crack tip radius,

tipr , is given (Ewards & Wanhill, 1986):

tipI Ir K K

2r 2 r 2 r

⎛ ⎞σ = + ⎜ ⎟

π π ⎝ ⎠ (6)

where I K is the stress intensity factor. The force acting on the cell rib can be obtained

when the integral is over the thickness of a rib, that is,


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/ 2

/ 222 2

tip

tip

r t

tip I I tip

r

r K K F r dr

r r r π π

+ ⎡ ⎤⎛ ⎞= +⎢ ⎥⎜ ⎟

⎝ ⎠⎣ ⎦∫ (7)

where t is the thickness of a rib. Using a Taylor series expansion and a first orderapproximation, the above equation can be expressed as:

*2.38 I

l t F K

lπ

⎛ ⎞= ⎜ ⎟⎝ ⎠

(8)

where * I K is the stress intensity factor of conventional foams and l is the rib length (refer

to Figure 13 (a)).

Figure 14 Structural and continuum views of a crack in a foam, suggesting the use of a non- zerocrack tip radius (after Choi & Lakes, 1996).

As the tension in the cell ribs is not important in comparison to bending except for foamswith very high density, the bending moment is considered as the major force applied tothe cell ribs (Choi & Lakes, 1996). The stress due to the bending moment is given by

32.12

F l

t

σ = . (9)

Substituting Eq.(8) into the above equation, the stress is

2

* 15.05 I

lK

t σ

π

⎛ ⎞= ⎜ ⎟⎝ ⎠

. (10)

The crack will grow if f

σ σ = , where σ is the fracture strength of the cell rib. Thus, the

fracture toughness of conventional foams, * I K , can be calculated by


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2

* 0.20 I f

t K l

lσ π

⎛ ⎞= ⎜ ⎟⎝ ⎠

. (11)

Since

*

/ ( / )

n

s t l ρ ρ α ∝ , therefore, the stress intensity factor of conventional foams isproportional to the normalized density, i.e.,

* *

0.19 IC

s f

K

l

ρ

ρ σ π

⎛ ⎞= ⎜ ⎟

⎝ ⎠ (12)

where * ρ is the density of a foam,s

ρ is the density of the solid from which the foam is

made, α and n are constants.

For the fracture toughness of re-entrant foams, the similar formulae as equations (11) and

(12) can be obtained but the special structure of this type of a material must be considered.The fracture toughness in non-conventional foams (i.e. re-entrant) can be expressed by(Choi & Lakes, 1996)

*1 sin( )20.10

1 cos 2

r

IC

s f

K

l

π ϕ

ρ

ϕ ρ σ π

+ − ⎛ ⎞= ⎜ ⎟

+ ⎝ ⎠ (13)

where * IC

K is fracture toughness of re-entrant foams and ϕ is rib angle related to the cell

shape. The detail of the derivation of equation (12) is in the work by Choi & Lakes (1996).From Eq.(11) and Eq.(13), the ratio of the fracture toughness of re-entrant foams to that ofconventional foams is given by

*

1 sin( )2

0.531 cos 2

r

IC

IC

K

K

π ϕ

ϕ

+ −=

+. (14)

Since the above model is established on the simplified model, for volumetric compressionratios of 2.5 and greater, the results may be overly optimized, because re-entrant foam hasa complex and irregular microstructure. Therefore, the effect of volumetric compressionratio on toughness7 is slightly complicated, depending on the annealing state of a material(Figure 15). Compared to that of conventional foam materials, the toughness is increasedby factors of 1.4, 1.5 and 1.7 with increases of volumetric compression ratio of 2.0, 2.5, 3.0,respectively (Choi & Lakes, 1992). For non-annealed materials, the toughness increaseswith volumetric compression ratio, but under annealed conditions, toughness increases upto volumetric compression ratio of ~2.0. Further increase in volumetric compression ratioleads to a decrease in toughness.

7 Toughness is here defined as the energy per unit volume to fracture (Choi & Lakes, 1992).


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Figure 15 Toughness as a function of permanent volumetric compression of the conventional andre-entrant copper foams: open symbols, non-annealed; solid symbols, annealed (afterChoi & Lakes, 1992).

3.4.2 Microstructural Morphology

The microstructure of the foam is complicated. Figure 16 shows the microstructures of theopen-cell and closed-cell conventional polyester urethane foams (Chan & Evans, 1997). Inthe closed-cell foam, most of the cell faces are closed off by thin membranes. The porousopen-cell foams allow free movement of air through-out the material when flexed. Auxeticfoams have a more complex, re-entrant geometry (Figure 17 (a)). Therefore, they are muchmore likely to deform by hinging and flexure rather than stretching in both tension (Figure17 (b)) and compression (Figure 17 (c)). Under tension, the cells are seen to expand

transversely under a longitudinal tensile force (Chan & Evans, 1997). The reason is thatauxetic foam is consisted of nodules interconnected by fibrils (Caddock & Evans, 1989).Also, conventional foams are made up of convex polyhedral cells, but auxetic foams havemuch more convoluted cell structures (Choi & Lakes, 1995; Chan & Evans, 1997), as shownin Figure 18. An example is the microstructure of UHMWPE is shown in Figure 19(Alderson & Evans, 1992).

3.4.3 Crack Resistance

Compared with non-auxetic materials, auxetic materials also have other special anddesirable mechanical properties. For example, if the material has a crack, when it is being


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pulled apart, it expands and closes up the crack. In other words, this type of materialshould possess more crack resistance to fracture. Also, it has high material resistance toshear strain. Shear resistance is particularly important in structural components such as

sheets or beams in building, cars and aircraft.

(a) (b)

Figure 16 Microstructures of the conventional polyester urethane foams: (a) Closed-cell (opticalmicrograph) and (b) Open-cell (SEM) (after Chan & Lakes, 1997).

(a) (b)

Figure 17 (a) and (b) (after Chan & Evans, 1997)


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(c)

Figure 17 Micrographs of the auxetic polyester polyurethane foams showing the elasticdeformations under different type of loads. (a) Unloaded; (b) Under tension and (c)Under compression (after Chan & Evans, 1997).

(a) (b)

Figure 18 Open cell polymer foams: (a) non-auxetic and (b) auxetic (after Choi & Lakes, 1995;Chan & Evans, 1997).


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Figure 19 Micrograph of the microstructure of auxetic UHMWPE (after Alderson & Evans,1992).

3.5

Damping and Sound Absorption

The negative Poisson's ratio foam presented shows an overall superiority regardingdamping and acoustic properties compared to the original conventional foam (Scarpa, et

al, 2004). Auxetic foams can have better sound absorption capacity than conventionalfoams at all levels of frequencies. The auxetic foams with smaller pore sizes absorb soundmore efficiently than with larger pores at the frequencies above 630 Hz (Howell, et al,1994). For example, the highest measurable ultrasonic attenuation value of auxeticmicroporous UHMWPE was 1.5 times the highest value of the microporous UHMWPEwith positive Poisson’s ratio and is more than 3 times that of conventional processedmaterials (Alderson, et al, 1997 and 2000). Its dynamic crushing performance is alsosignificantly superior to normal foam, suggesting a possible use in structural integritycompliant elements.


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4. Manufacturing Methods

As stated above, materials with NPRs have properties distinctive to those of conventionalproperties and these materials can be made from a variety of polymers or metals (Lakes,1987; Friis, et al, 1988). There are as many different routes as there are materials. Someroutes rely on transforming non-auxetic materials into auxetic foam, whereas othersemploy standard techniques but with novel material architecture to achieve the auxeticeffect (honeycombs and fibre-reinforced composites). Still others require noveldevelopment of existing processing routes for conventional materials to produce auxeticfunctionality. In this literature review report, the recipe or procedure of making a materialwith NPR is directly taken from Lakes’ and other people’s published papers. This recipecan be used for educational or research purpose only. Also, the manufacture method ofauxetic fibres (e.g. polypropylene-PP), which was proposed by Alderson et al (2002), is

described here.

Other technical methods can also be used to manufacture materials with NPR such as re-entrant cell structure material (i.e. one of polymeric foams), but for different foammaterials, the procedures or recipes are different. For example:(1) For thermoplastic polymer foams, in the procedure a triaxial compression is applied bya factor of 1.4 to 4 in volume, followed by heating to a temperature above the softeningpoint, then by cooling under a volumetric constraint.(2) For metallic foams, the procedure consists of applying uniaxial compression at roomtemperature until the foam yields. Additional compression is then applied sequentially ineach of the three-orthogonal direction until the desired volume change is achieved.

4.1 Manufacture of Auxetic Foams

4.1.1 Polymeric Foams

One way of obtaining a negative Poisson’s ratio is to use a re-entrant cell structure becausethe properties can be controlled by processing techniques through changing the cell shape.The method used for the manufacture of auxetic samples contains four stages: (1)compression; (2) heating; (3) cooling and (4) relaxation (Lakes, 1987). To transform aconventional foam into an auxetic one using this technique requires that the foam must be

simultaneously compressed in three dimensions to force the cell ribs to buckle. However,different types of polymeric foams (e.g., open or closed) require different heating time andtemperatures. More details of the manufacture of the auxetic foams using this techniquecan be found in Chan & Evans’s work (1995 & 1997). The recipe for manufacturingdemonstration auxetic samples can be seen in Appendix A.

However, Lakes indicated: “Each kind of polymer foam has its own softening point andtransition temperature. These instructions are for polyester and polyether polyurethanefoams. For other foams the transition temperature is to be found empirically. ScottIndustrial Foam with 10 to 20 pores per inch works best; it is reticulated open cell foamused for air filters. Scott foam with smaller pores also works well. Open-cell polymeric


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packing foams can be used; they may be more sensitive to processing temperature andhumidity. Initial foam density should be low. Foam of 0.043 g/cm 3 [2.7 lb/ft3] is suitable.If the initial solid volume fraction is too high, there may be insufficient space in the

structure to achieve the required permanent compression. Closed-cell foam can beprocessed but the procedure is more difficult.” A route to convert a closed-cell polymerfoam to an auxetic foam has been reported (Martz, et al, 1996).

4.1.2 Metallic Foams

Certain types of metallic foams such as copper foam can be transformed into auxetic or re-entrant materials by successive applications of small increments of plastic deformation inthree orthogonal directions. For manufacturing metallic foams with NPR, Lakes made thefollowing comments:

“Ductile metal foams, such as those based on aluminium or copper, can be converted intoNPR foams as follows. The resulting properties are given in the manuscripts referred to inthe main Poisson page. Use a vice or other compression device to plastically deform themetal foam in one direction by about 5% or less. Repeat in another direction at rightangles. Repeat in a third direction at right angles. Repeat the entire process until thevolume of the foam is reduced by a factor between two and four. The optimum valuedepends on the initial density of the foam. If you have made these foams, you deserve abrass badger. This brass badger served on the battleship USS Wisconsin; it is now in theState Capitol in Madison. The nose of the badger is shiny because people like to squeezeit.”

4.2

Manufacture of Auxetic Fibres and Composites

The flow chart for the process is shown in Figure 20, where the process, which wasproposed by Webber et al (2000) and Alderson et al (2002 & 2005), has several stages:(1) The first stage is to compact the polypropylene (PP) powder, which should be finely

divided with an average particle size between 50 and 300 μm.(2) In the following stage, compaction takes place within the barrel (15 mm of diameter) ofthe processing rig, which is fitted with a blank die, as shown in Figure 21.(3) Then the compacted rod is reinserted into the barrel, sintered and extruded.

After these three stages, the auxetic fibres are made. This type of auxetic fibre possesses -

0.22 Poisson’s ratio and are less than 1 mm of the diameter, produced by a continuousprocess, where conventional melt spinning is used, as shown in Figure 22. The details ofthe process are in the paper by Alderson, et al (1995 & 2002). This is a relatively simpleprocess to produce auxetic fibres, based on the modification of a conventional polymerprocessing technique. However, as Alderson indicated, the key difference is that the fibre

is much thinner (only ~ 280 μm), compared with 1 mm of the conventional PP cylinders.This implies that the geometry and deformation mechanisms of the microstructure areresponsible for the auxetic behaviour.


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Manually maintain applied pressure at20 MPa for 20 minutes

Heat processing rig fitted with extrusiondie to 159oC

Heat processing rig to 80oC with blankdie inserted

Pour finely divided PP powder into barrel

Leave for 10 minutes

Begin applying pressure at a controlleddisplacement rate of 20 mm/min

Remove compacted rod from barrel andallow cooling in air to room

Reinsert compact rod into barrel

Sinter for 20 minutes

Immediately extrude at 500 mm/minwith temperature held at 159oC. Diegeometry used: entry diameter 15 mm,exit diameter 9 mm, core semi-angle30o and capillary length 3.4 mm

Figure 20 Flow chart of the process to produce auxetic polypropylene fibres (after Webber, et al,2000; Alderson, et al, 2002 & 2005).

Figure 21 Schematic diagram of processing rig used to produce auxetic polypropylene fibres(Webber, et al, 2000; Alderson, et al, 2002 & 2005).


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Figure 22 Schematic diagram of melt extruder used to produce auxetic polypropylene fibres

(Webber, et al, 2000; Alderson, et al, 2002), where 1-polymer hopper; 2-barrel; 3- Archimedean; 4-screw feed zone; 5-screw compression zone; 6-screw metering zone; 7-cavity transfer mixing zone (adaptor zone); 8-die zone; 9-cooling roller; 10-nip roller;11-air knife; 12, 13,14-rollers; 15-guide rail; 16-windup.

4.3 Other Methods and Examples

Auxetic microporous polymers, for example, microporous PTFE, is based on theconventional powder processing techniques of sintering (Alderson, et al, 1995) andextrusion (Neale, et al, 1995) of the polymer powder. The three steps of compaction,

sintering and extrusion are necessary to achieve auxeticity because the microstructureconsists of an interconnected network with nodules (particles) and fibrils, as shown inFigure 23. Feature sizes are typically at the order of 20 μm (Caddock & Evans, 1989).

Figure 23 SEM micrograph of the auxetic expanded PTFE microstructure (after Evans, 1989;Evans & Caddock, 1989).


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A novel thermal processing route, for UHMWPE used to achieve this complexmicrostructure, is a batch process based on conventional polymer powder processingtechniques of sintering of the starting powder, which gives rise to fibrillation (Alderson &

Evans, 1992). An additional initial compaction stage can be used solely to impart somedegree of structural integrity to the extrudate and extrusion through a conical die, butadapted so that there is only partial melting This means the properties of the polymers canbe tailored to fit the applications required and, by varying certain processing parameters,to produce everything from structural auxetic polymers, down to very auxetic, lowmodulus polymers (Evans & Alderson, 1992; Pickles, et al, 1996; Alderson, et al, 1997). Asthe UHMWPE (with a Young's modulus of ~0.2 GPa) is comparable with conventionalthermoplastic polymers, therefore, this type of material is potentially suitable for use instructural applications (Evans & Alderson, 1992).


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5. Potential Applications and Limitations

NPR materials offer a new direction for achieving unusual and improved mechanicalperformance. Studies, with support from NASA and Boeing, have demonstratedenhancements in mechanical properties for auxetic materials, including shear resistance(Choi & Lakes, 1992a & 1992b), indentation resistance (Lakes & Elms, 1993; Chan & Lakes,1998) and fracture toughness (Choi & Lakes, 1996). The investigation of dynamic effect,partially founded by the US Office of Naval Research, has also demonstrated that soundand vibration absorption have been enhanced (Chen & lakes, 1993 & 1996). Withcontinuous progress in the fabrication and synthesis of a wider range of such excitingmaterials there is huge potential for application in industrial and defence sectors.

Generally, applications of materials with NPR are mainly based on:

(i) Unusual Poisson's ratio;(ii) Superior toughness, resilience, and shear resistance, which has been observed in thesematerials, and(iii) Acoustic properties associated with the vibration of ribs in the material.

5.1 General Applications

The Poisson's ratio influences deformation kinematics in many ways, which may be useful,and it influences the distribution of stresses. For example, stress concentration factors arereduced in some situations and increased in others, when Poisson's ratio is negative.

Materials with NPR can enhance the performance of piezoelectric transducers. Auxeticmaterials are also likely to find uses in applications such as fasteners, car bumpers, soundproofing and shin pads.

5.1.1 Sensors

Materials with NPR can advantageously be used in the design of hydrophones and othersensors (Avellanads & Swart, 1998), because the low bulk modulus makes them moresensitive to hydrostatic pressure. For example, the sensitivity is increased by almost oneorder of magnitude with NPR of -1, compared to a material with a ordinary Poisson’s ratioof 0.3 (refer to Eq.(5)).

5.1.2 Biomedicine

Artificial blood vessel is a typical example for the medical application. If the blood vesselis made of conventional material, it tends to undergo a decrease in wall thickness as thevessel opens up in response to a pulse of blood flowing through it (Figure 24 (a)). Thiscould lead to rupture of the vessel with potentially catastrophic results. However, if anauxetic blood vessel is used, the wall thickness increases when a pulse of blood flowsthrough it (Figure 24 (b)). In addition, a dilator for opening the cavity of an artery orsimilar vessel has been described for use in heart surgery (angioplasty) and relatedprocedures (see Figure 25). The coronary artery is opened up by the lateral expansion of a


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flexible auxetic PTFE hollow rod or sheath under tension. More potential applicationsinclude surgical implants (Friis, 1992), and suture anchors or muscle/ligament anchors,where the additional benefit of a porous structure should promote bone growth (Evans &

Alderson, 2000).

Figure 24 Schematic diagram of deformation behaviour of artificial blood vessels: (a) Conventionalmaterial and (b) Auxetic blood vessel (after Evans & Alderson, 2000).

Figure 25 Dilator employing an auxetic end sheath. Insertion of finger and thumb apparatuscauses the auxetic sheath to extend and expand laterally, thus opening up thesurrounding vessel (after Moyers, 1992; Alderson, 1999).

5.1.3 Auxetic Fibre Reinforced Composites

It is expected that auxetic reinforcing fibres should enhance fracture resistance ofcomposites. It is well known that the interface between matrix and fibres is the weakestpart of a composite material (Figure 26 (a)). Fibre pull-out is a major failure mechanism infibre reinforced composites. For example, a unidirectional composite loaded in tension willundergo lateral contraction of both the matrix and fibres in conventional compositematerials, leading to failure at the fibre/matrix interface as shown in Figure 26 (b).However, replacing of conventional fibre by auxetic fibres could delay the pull-out offibres, potentially helping to resist crack growth, because the possibility of maintaining the


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interface by careful matching of the Poisson's ratios of the matrix and fibre leading to fibreexpansion during pull-out, as shown in Figure 26 (c) (Evans, 1990; Stott, et al, 2000).

(a) (b) (c)

Figure 26 Fibre pull-out in composites (after Stott, et al, 2000; Alderson, et al, 2005).

5.1.4 Structures

The counterintuitive property of auxetic materials, namely, lateral expansion(compression) under longitudinal tensile (compression) loads, is essential from the point ofview of modern technology. Many applications for auxetic materials have been designedin various fields of human activity, from vascular implants, strain sensors, shock and

sound absorbers, "press-fit" fasteners, gaskets and air filters, to fillings for highway joints.Materials containing inclusions of negative stiffness constitute another class of systemswith unusual mechanical properties. The recent interest in such systems has its origin intheir very high damping properties.

The mechanical properties of auxetic honeycombs are highly sensitive to themicrostructure unit cell geometric parameters. This is a feature that could be used todesign optimised sandwich structures for various applications. As an example, regularhexagonal honeycombs do not excel in sound absorption applications. Selectedcombinations of microstructure properties of auxetic honeycombs have been proven toincrease the transmission loss factors inside cylindrical shells. Wave dispersion properties

can also be custom tuned by varying the auxetic microstructure layout.

5.2 Potential Applications in Aerospace and Defence

Some materials with such anomalous (i.e. NPR) properties have been used in realapplications such as pyrolytic graphite with NPR of -0.21 for thermal protection inaerospace (Garber, 1963), large single crystals of Ni3Al with a minimum Poisson’s ratio of–0.18 in vanes for aircraft gas turbine engines (Baughman, et al, 1998; Nakamura, 1995),and so on. Also, the new auxetic materials and processing routes have been continuallydeveloped in recent years. Patent applications have been also reported from organisations


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such as Toyota, Yamaha, Mitsubishi, AlliedSignal Inc, BNFL and the US Office of NavalResearch. All of these applications are related to the emerging potential of these materials.

Auxetic fibres can be employed as reinforcement, leading to enhanced impact andindentation resistance and superior energy absorption in a textile. Therefore, because oftheir unique properties, auxetic materials are potentially attractive for applications inprotective clothing and others for military and homeland security, such as superiorperformance outfits, combat jackets and body armour (e.g., bullet-proof helmets, bullet-proof vests etc).

5.2.1 Smart or “Intelligent” Textiles

Defence protective clothing could also benefit from these materials, leading to higher-performance garments right across the range from thermal underwear to combat jackets

and body armour.

Currently, protective materials normally need to be up to a centimetre thick, and so arevery stiff, heavy and inflexible. However, body armour made from auxetic materials couldgive the similar protection for military personnel in the battlefield, but it would be thinnerand lighter. Auxetic materials have another special property in their behaviour when bent.For example, if a sheet of any material is bent downwards, the top surface is inevitablyslightly stretched. A normal material responds to this by attempting to shrink in theperpendicular direction, so the edges tend to curl upwards, leading to formation of asaddle shaped surface (anticlastic curvature), as shown in Figure 27 (a). But in auxeticmaterials the response is to cause the edges to curve downwards, that is convex shape

(dome-like shape), which is the same direction as the bending force (Figure 27 (b). Thispeculiar function of auxetic materials is useful to manufacture better body armours,because auxetic body armour could give the same safeguard but thinner, lighter, andconform better to the synclastic double curvatures of the human body (Burke, 1997;McMullan, 2004). Also, the convex shapes are more appropriate than saddle shapes forsandwich panels for aircraft or automobiles (Lakes, 1987 & 1993b).

(a) (b)

Figure 27 Bending behaviours of (a) Curvature behaviours in non-auxetic and (b) auxetic (doublecurvature-convex shape) (after Lakes, 1987; Evans, 1990; Cherfas, 1990).


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5.2.2 Bullet-Proof Helmets and Vests

Another promising application area is using auxetic polymers to make bullet-proof

helmets or vests more resilient to knocks and shrapnel. When an auxetic helmet suffers animpact from one direction, material should flow in from other directions to compensate forthe impact. Therefore, head injuries may be prevented or be less severe. The DefenceClothing and Textile Agency (DCTA) in Colchester, which is responsible for research intohigh-tech clothing for the military, has been looking into the use of auxetic textiles formilitary purposes. But, there is still a lot to be learnt and it is not clear what would happenunder a high-speed impact such as a bullet (Burke, 1997). However, if the research workon this issue were successful, it would open up a massive market in the world. Forexample, the UK alone has a need for half a million helmets (Burke, 1997).

Mitsubishi has patented a ‘narrow passage moving body with highly efficient movement’

— in other words a bullet — in which one component is made of an auxetic material sothat the overall object has a Poisson’s ratio of zero (Figure 28). In this case the movement ofthe projectile down a barrel, for example, is helped because the sideways expansionarising from the thrusting force is reduced. Auxetic materials have also been identified ascandidate materials for use in electromagnetic launcher technology to propel suchprojectiles. And the intended recipient of the projectile might benefit from a bullet-proofvest and other personal protective equipment formed from auxetic material because oftheir impact property enhancements.

Figure 28 Schematic of the principle of auxetic material used to human protection (After Alderson, 1999).

5.2.3 Fasteners and Rivets

Because auxetic materials expand sideways when pulled, hence they would be ideal formaking fasteners and rivets. Insertion of the auxetic fastener is facilitated by the lateralcontraction under compression, while removal of the fastener is resisted since the fastener


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expands and jams itself more tightly in the hole under tension (Choi & lakes, 1991). Figure29 shows the relationship between the load and displacement during the insertion andremoval of the fastener (copper re-entrant foam). During insertion, the load-displacement

curve shows an initial sharp increase in the load and then more gradual increase until themaximum displacement is reached. During the removal, the load is sharply increased andthe fastener breaks at a displacement of 2.8 mm and a load of 160 N. The fracture surfacewas in the body of the core, away from the socket and embedded grip ends.

Figure 29 Load as a function of displacement for experimental insertion and removal of fastenercore, which is made of copper re-entrant foam (after Choi & Lakes, 1991)

5.2.4 Energy Absorption Material for the Protection of Airborne Cargo Drops

Currently, Energy Dissipating Material (EDM) is used to cushion the impact of all airbornesupplies in order to ensure that they arrive on the ground safely and are fully functional.The EDM is a paper product comprising a Kraft paper honeycomb core 75 mm thick, faced

on both sides with Kraft paper. The idea is that on contact, the EDM crushes to at least70% of its original thickness, dissipating some of the impact, and releasing trapped air toavert a massive deceleration or bounce that could damage the cargo (Connections, 2005).

Conventional polymeric foams (e.g. polyethylene) are available in a range of densities forpacking and cushioning applications and for sports equipments. But materials with NPR(e.g. auxetics) possess much better impact resistance, indentation resistance and energyabsorption properties. Therefore, a material with NPR might be potentially applied toaircraft equipment protection such as cargo drop to prevent the damage due to highenergy absorption (Athiniotis & Cannon, 2006). However, the biggest question for the


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application is whether such a material is commercially available and its strength satisfiesthe requirements as a structural material in this particular application.

5.2.5 Other Applications

Apart for the above applications, materials with NPR should have more applications inaerospace industry. For example, from the mechanical point of view, the Poisson’s ratiodoes not depend on scale, so auxetic materials should not be difficult to be extended tostructures built from conventional components that would “open up” when stretched.These “expandable” structures can be particularly useful for the manufacture of spacestructures such as large antennas and sun shields that could be launched into space in aclosed compact form and then “open up” at a later stage in space (Grima, et al, 2005).

As mentioned in Sec.3, auxetic materials have higher resistance against shearing (tearing

force) and twisting than conventional materials. These properties are particularlyimportant for structural components, which may fail under shear strain such as beams inbuildings, sheets used in aircraft or cars etc).

Smith from the US Office of Naval Research showed that the sensitivity of a sonar receiverwas increased by an order of magnitude by replacing a non-auxetic matrix with anisotropic auxetic matrix (Smith, 1991). A further advantage of using auxetic materials istheir behaviour when bent. As mentioned in Sec.5.2.1, the double curvature is one of theimportant deformation mechanisms in auxetic materials. This feature can be used inmoulding and shaping sandwich panels for aircraft components such as nose cones or carbody parts.

5.3 Limitations

As stated above, auxetic materials potentially have many applications, because of theirwonderful properties compared to conventional (i.e. non-auxetic) materials. However,they also have their own limitations like other materials.

The special microstructural features for auxetic materials need space to allow the “hinges”to flex, or the “nodules” to spread out. The materials often need substantial porosity.Therefore, materials with negative Poisson’s ratio are substantially less stiff than the solids

from which they are made and this causes limitations on the structural applications of thematerials with negative Poisson’s ratio (Jones, 2001). For example, they are normally notstiff enough or not dense enough for load-bearing applications.


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6. Conclusions and Recommendations

Materials with NPR show unique properties, compared to ordinary materials such asenhancement of shear modulus, indentation resistance or plane strain fracture toughness,although they have less stiffness. Therefore, they have many potential applications toDefence such as personal protective equipment (e.g., protective clothing, body armour,bullet-proof vest, etc) and others (e.g., “smart” sensors, sonar, panels etc). Also, thesematerials could potentially be used to build completely new structures with specialfunctions. However, more research work needs to be done for further understanding ofthese materials and applications to real components.

For future work, experimental tests need to be carried out to further understand thebehaviours of these types of materials. Also, for future work it is necessary to collaboratewith researchers from textile, chemical & biological areas to explore the potentialapplications for protecting military personnel from injury, or chemical & biological attacksfrom enemy or terrorists.

7. Acknowledgements

This work was founded by Air Vehicles Division (AVD), DSTO and was part of the IdeasProgram in AVD. The author sincerely thanks the support from AVD and Mr. D.Lombardo, a task manager of the program. The author also acknowledge Mr. Athiniotisand Cannon for their valuable comments and suggestions.

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No.8, pp.33-39, 1995.

Nur, A. and Simmons, G., The effect of saturation on velocity in low porosity rocks, EarthPlanet Sci. Lett., Vol.7, pp.183-193, 1969.

Pickles, A.P., Webber, R.S., Alderson, K.L., Neale, P.J. and Evans, K.E., The effect of theprocessing parameters on the fabrication of auxetic polyethylene. Part I. The effect ofcompaction condition, J. Mater. Sci., Vol.30, pp.4059-4068, 1995.

Pickles, A.P., Alderson, K.L. and Evans, K.E., The effects of powder morphology on theprocessing of auxetic polypropylene PP of negative Poisson’s ratio), Polym. Eng. & Sci.,

Vol.36, No.5, pp.636-642, 1996.

Scarpa, F., Ciffo, L. G. and Yates, J. R., Dynamic properties of high structural integrityauxetic open cell foam, Smart Mater. Struct, Vol.13, No.1, pp.49-56, 2004.

Smith, C.W., Evans, K.E. and Lehaman, F., Strain densification during indentation inauxetic foams, Cell. Poly., Vol.18, pp.79-101, 1999.

Smith, W.A., Optimizing electromechanical coupling in piezocomposites using polymerswith negative Poisson’s ratio, Proc. of IEEE Ultrasonic Symp., IEEE, pp.661-666, 1991.

Stott, P.J., R. Mitchell, K. Alderson and A. Alderson, A growing industry, Materials World,vol. 8, pp.12-14, 2000.

Webber, R.S., Alderson, K.L. and Evans, K.E., Novel variations in the microstructure of theauxetic microporous ultra-high molecular weight polyethylene. Part 1: Processing andmicrostructure, Poly. Engng. Sci., Vol.40, No.8, pp.1894-1905, 2000.

http://www.ptfe.gatech.edu/faculty/mcmullan/paper.phphttp://www.ptfe.gatech.edu/faculty/mcmullan/paper.php


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Appendix A: Recipe for Polymeric Foams

Note: The following procedure is adapted from Lakes’ published paper (1987a).

The mould : We have used aluminium square tube, 1" square, for a mould. If too large amould is used, heat transfer will be poor, and only the outer portion of the foam will betransformed.

(1) Preheat furnace to about 160-170 deg C.

(2) Either measure or mark foam for later determination of strains. Mark foam in all 3

orthogonal directions, i.e., two adjacent corners and down one side.(3) [optional: this is not necessary if sufficient care is taken in removing wrinkles]

Lubricate sides of square aluminium tube with vegetable oil. Spray cooking oil (PAM) canalso be used, but does not seem to work better. DO NOT use a petroleum distillate baselubricant; it will smell terrible when heated.(4) Stuff the foam in the tube. It works well to start the foam slightly by hand and thenwork it up gently with a tongue depressor to remove wrinkles.(5) Pull the foam a little on both ends to get rid of creases created by stuffing the material.This procedure will result in a pre stretched sample in the tube. The actual original lengthof the sample must be used when determining the amount of pre compression to apply.(6) Place the compression device and end plates on the stuffed tube.(7) If the desired specimen length is less than the square tube size, select the correct lengthof cut tubing [pipe] within the mould to compress the foam longitudinally by the same

amount as transversely. Alternatively, cut the foam proportionally longer than the squaretube length and do not use pipe.(8) Push the pipe down on the loose end plate such that the foam is compressed evenly atthe end. Try not to push too fast; this may contribute to the uneven distribution ofcompression along the length of the specimen.(9) Gently tighten down the side screws to hold the cut pipe in place.(10) Place assembly in centre of furnace or oven. A kitchen oven is sufficient.(11) Leave the foam in the oven for a predetermined amount of time. The gray polyesterfoams transform better at a slightly lower temperature for a longer amount of time, about20 minutes maximum. The white/cream coloured polyether foam seems to be moresensitive with respect to melting together; 17-18 min. is appropriate.

(12) Remove and cool the specimen completely. Taking the specimen out of the mouldbefore complete cooling may result in premature release of the pre compression. It may behelpful to release foam ribs which have stuck together: stretch the specimen gently in eachof three directions. Congratulations! You have made negative Poisson's ratio foam (alsocalled anti-rubber, dilational material, or auxetic material).(13) Measure the amount of permanent compression retained by the specimen by eithermeasuring the new distance between the marks or by measuring the size of thetransformed sample.(14) Other kinds of moulds are possible and have been used successfully by others.


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Literature Review: Materials with Negative Poisson’s Ratios and Potential Applications toAerospace and Defence

Qianchu Liu

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Literature Review: Materials with Negative Poisson's Ratios andPotential Applications to Aerospace and Defence

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Q. Liu

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DSTO Defence Science and Technology Organisation506 Lorimer StFishermans Bend Victoria 3207 Australia

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August 2006

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18. DSTO Research Library Thesaurus

Materials, Foams, Polymers, Composites, Properties

19. ABSTRACT

An auxetic material exhibits exceptional features, which are different from a conventional material. That is, theauxetic material gets fatter when it is stretched, or becomes smaller when it is compressed, because it has anegative Poisson’s ratio. This report briefly reviews the latest advances in research work in auxetic materials,structural mechanisms, properties and applications, particularly in aerospace and defence.

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